A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively ______.

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A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively (0, – 10) and (4, 0). Explanation: Let the coordinates of P and 0 (0, y) and (x, 0), respectively. So, the mid-point of P(0, y) and Q(x, 0) is M((0 + x)/2, (y + 0)/2) ...`[∵ "Mid-point of a line segment having points" (x_1, y_1) "and" (x_2, y_2) = ((x_1 + x_2)/2, (y_1 + y_2)/2)]` But it is given that, mid-point of PQ is (2, –5). $\therefore$ 2 = (x + 0)/2 And – 5 = (y + 0)/2 $\Rightarrow$ 4 = x and – 10 = y $\Rightarrow$ x = 4 and y = – 10 So, the coordinates of P and Q are (0, – 10) and (4, 0). [Solution diagram: 270584_solution_1.png]

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